Being a mathematics education researcher, my focus lies in delving into how math instruction significantly impacts students’ learning, especially when it comes to grasping mathematical concepts rather than just memorizing procedures. Conceptual understanding is the key here, as it involves reasoning behind the math rather than just following steps to reach an answer.
In traditional mathematics classrooms, students are often presented with steps and procedures to solve math problems, with an expectation to memorize and reproduce these steps independently. This approach results in a decline in students’ agency, knowledge, and ability to apply mathematical concepts in real-world scenarios. Moreover, it hinders their confidence in tackling math problems and impedes their progression to more advanced mathematical concepts.
While procedural fluency is important, conceptual understanding acts as a framework for students to establish mental connections between various math concepts. It enables them to relate new ideas to existing knowledge, paving the way for a deeper understanding of advanced mathematics. Thus, the shift towards focusing on concepts rather than procedures is essential to enhance mathematics achievement.
Emphasizing Concept over Procedure
Conceptual understanding goes beyond rote memorization; it builds upon existing knowledge, emphasizing students’ ability to justify and explain mathematical concepts. Procedural fluency, on the other hand, revolves around following steps to arrive at an answer with accuracy.
When preparing students for advanced mathematical concepts, it is crucial to analyze how they engage with problems presented in class and how these problems contribute to either their conceptual understanding or procedural fluency. For instance, when presented with two math questions, one requiring reasoning and the other relying on procedural knowledge, the distinction between the two becomes evident.
As educators, our goal should be to guide students towards conceptual understanding rather than mere procedural proficiency. Providing opportunities for exploration, fostering productive struggle, encouraging explanation of thought process, and facilitating connections between existing and new knowledge are essential components in this journey.
Inquiry-based instruction, which places students at the center of learning, aids in developing conceptual understanding by empowering students to think critically and devise their solutions and strategies. By incorporating strategies that promote conceptual understanding into our teaching practices, we can steer students towards becoming proficient mathematical thinkers.
Advancing Conceptual Understanding
Teaching for conceptual understanding requires deep content knowledge and the ability to make real-time connections between student responses and mathematical concepts. It demands flexibility and creativity from educators to address the diverse responses students may offer while solving math problems.
Thankfully, various instructional strategies have been developed through mathematics education research to enhance conceptual understanding in students:
Engage with Open-Ended Tasks
Open-ended tasks offer students multiple entry and exit points, allowing for varied approaches and solutions. Students can choose strategies that best suit them, while educators can guide them towards more efficient reasoning paths. Open-ended questions also facilitate comparison of different thinking approaches, fostering a deeper understanding of mathematical concepts.
Focus on Unit Operations
Understanding how units operate within a problem is crucial for students’ conceptual understanding. By exploring the relationship between units and visualizing them, students can grasp mathematical concepts more effectively. Encouraging students to reflect on unit operations enhances their overall mathematical reasoning skills.
Promote Mathematical Discourse
Encouraging mathematical discourse among students and between educators and students is vital for promoting conceptual understanding. By leveraging existing math knowledge as entry points, educators can facilitate meaningful conversations and help students build upon their mathematical foundations.
By infusing conceptual understanding into math lessons and letting procedures evolve from this understanding, we can empower students to enhance their mathematics achievement and develop a deeper appreciation for mathematical thinking.
